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# Elemental Theory and the Realm of Forms

#### by Jeremiah Genest

The copyright of this article remains with the original author. Articles may be copied or distributed freely for personal non-profit use, provided that the author is properly credited.

A great deal of recent discussion has been about the elements and the need for requisites. In particular whether ice needs a Terram requisite or is even Terram. I would like to view this process by looking at the subject the way a medieval scholar would, and thus what I would consider an opinion your average mage would hold.

First I will consider Plato. Until the thirteenth century Plato dominated the Medieval world (and the world of late antiquity before that). Bonisagus would certainly have been aware of Plato (or the Latin redactions of his thought). Furthermore, Hermetic theory shows a heavy bias toward Platonism, especially in its use of the Realm of Forms, not only for Creo but throughout the published material. Rather than give a long essay on Plato's realm of Forms and his cosmology, I will instead focus on his idea of elements. More detailed information can be acquired elsewhere.

For Plato the cosmos was constructed on geometrical principles. He took over the four roots or elements of Empedocles: earth, water, air and fire. Under Pythagorean influence, he reduced them to something more fundamental - -- triangles. He thus formulated a "geometrical atomism." As two-dimensional figures, triangles are of course incorporeal; however, if suitably combined, they can be made into three-dimensional corpuscles, each different shape corresponding to one of the elements. There are five, and only five, regular geometrical solids (symmetrical solid figures formed of plane surfaces, all identical); these are the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron. Plato associated each element with a figure-fire with the tetrahedron (the smallest, sharpest and most mobile of the regular solids), air with the octahedron, water with the icosahedron, and earth with the most stable of the regular solids, the cube. Finally, Plato found a function for the dodecahedron (the regular solid closest to the sphere) by identifying it with the cosmos as a whole.

This scheme allows the elements to mix in various proportions to produce variety in the material world. More importantly for Ars Magica, it allows for transmutation of the elements from one to another, thus accounting for Muto spells (and other magics). For example, we can dissolve a single corpuscle of water (the icosahedron) into its twenty constituent equilateral triangles, which can then recombine, into, say, two corpuscles of air (the octahedron) and one of fire (the tetrahedron). Only earth, which is composed of squares (and the square divided diagonally does not yield equilateral triangles), is excluded from this process of transmutation. Furthermore, note that ice was always considered a water. Plato pointed out that an icosahedron (or an octahedron) for that matter cannot be broken down into a square. Thus ice is just water that is at rest. At no point does he ever confuse it with earth. Nor will you find a single platonic thinker who would hold this (neither middle, neoplatonism nor any other Platonism).

After the reception and assimilation of Aristotle's philosophy in the twelfth and thirteenth centuries, the principles in question were broadly Aristotelian - though obscurity, incompleteness and inconsistency in the various Aristotelian texts where these principles were set out left plenty of room for further articulation of the theory and for discussion and debate about the fine points. Let us begin with a brief review of some of the basics of Aristotelian natural philosophy.

According to Aristotle, all objects in the terrestrial realm ("substances" he called them) are composites of form and matter. Form, the active principle or agent, bearer of the properties of the individual thing, combines inseparably with matter, the passive recipient of the form, to produce a concrete corporeal object. If the object in question is a "natural" object (as opposed to one produced artificially, by an artisan), it also has a nature (determined primarily by its form but secondarily by its matter), which disposes it to certain kinds of behavior. Thus fire naturally communicates warmth, rocks naturally fall (if lifted out of their natural place), babies naturally grow and mature, and acorns naturally develop into oak trees. These natures we discern through long and persistent observation: whatever cannot be the product of chance (because of the regularity of its occurrence) or of artifice (because no artificer had anything to do with it) must be the result of nature. Because natures are the determining factors in all cases of natural change, they are necessarily of great interest to the physicist or natural philosopher.

Aristotle's medieval followers, contemplating this scheme, identified two kinds of forms - one of them associated with essential properties, the other with incidental properties. The defining characteristics of a thing, which make it what it is, are conveyed by what came to be called its "substantial form." Substantial form combines with absolutely property-less first matter to give being or existence to a substance and to endow it with those properties that make it the kind of thing it is. However, besides essential properties, every substance also has properties of an incidental or accidental sort, associated with "accidental form." Thus the family dog may be short-haired or long-haired, lean or fat, friendly or ferocious, housebroken or not, and yet it retains the characteristics (supplied by its substantial form) that enable us to identify it unmistakably as a dog.

Aristotle's theory of form, matter and substance is nicely exemplified in his theory of the elements. Aristotle accepted the position of his predecessors, Plato and the pre-Socratics, to the effect that the familiar materials or substances of everyday experience are complex rather than simple. That is, sensible things in the sublunar world are compounds or mixtures, reducible to a small set of fundamental roots or principles, called "elements." Aristotle adopted Empedocles' and Plato's list of four elements - earth, water, air and fire - and argued that these combine in various proportions to produce all of the common substances. Aristotle agreed with Plato that the four elements are not fixed and immutable, but undergo transmutations; and the scheme that explained how this was possible was his theory of form and matter.

Each of the elements, he argued, is a composite of form and matter; since the matter in question is capable of assuming a succession of forms, the elements can be transformed onto one another. The forms instrumental in producing the elements are those associated with the four primary or "elemental" qualities: hot, cold, wet and dry. Primary matter informed by coldness and wetness yields water; and so forth. This primary matter has the capacity to receive any of the four elemental qualities. Therefore if the quality of dryness in a piece of the element earth yields to wetness through the action of a suitable agent, that piece of earth will cease to exist, and an appropriate amount of the element water will take its place. Aristotle argued that such transformations are occurring constantly, and the elements are therefore constantly being transmuted one into another. Changes of this kind proved capable of accounting for many of the familiar phenomena that we associate today with the disciplines of chemistry and meteorology.

The basic form-matter theory was easily understood, but its application to the real world posed a variety of problems. The world seemed to contain a hierarchy of forms and matters, and the Aristotelian definitions outlined above worked better at some levels than at others. Aristotle's definition of matter as the totally unqualified recipient of forms applies nicely to the constitution of the elements: the matter that receives the elemental forms of the primary qualities (hot, cold, wet, dry) is totally without properties of its own, apart from the ability to receive the elemental forms. Of itself, it is imperceptible, unknowable, and without actual existence. Aristotle, referred to this as "primary matter." Accidental forms are imposed on matter that already has independent, substantial existence: the marble out of which a statue is to be made exists as a concrete thing, with a variety of properties (size, shape, colour, density and hardness), before the sculptor endows it with the accidental forms that make it into a specific statue. In the same way, the hair that turns gray (thus serving as the matter for the accidental form of greyness) was already a substantial thing, with specific, identifiable characteristic, before it changed colour. Reflection on problems such as this caused Aristotle's ancient and medieval followers to sharpen his definitions and to clarify the distinction between the insubstantial primary matter of the elements and the substantial secondary matter encountered in cases of accidental change.

The matter-form theory was elaborated in Islam by Avicenna (Ibn Sn, 980-1037) and Averroes (Ibn Rushd, 1126-98) in ways that would prove influential in the West. The two Muslim commentators thought it impossible to derive the elements from the imposition of the elemental forms directly on primary matter. An intermediate step was required, which would first invest the primary matter with three-dimensionality. To this end, they developed the notion of "corporeal form," which must first be imposed on primary matter to yield a three-dimensional body. The elements emerge, then, when this three-dimensional body (a kind of secondary matter) receives the elemental forms. The idea of corporeal form was transmitted to Christendom, where it proved both influential and controversial. Robert of Grosseteste adopted this position when he identified corporeal form with light.

Aristotle had placed form and matter on essentially equal footing - neither was subordinate to the other, and each had its function - but this balance proved difficult to maintain. Within the Neoplatonic tradition (Avicenna is a good example) there was a tendency to demote matter, to see it as virtual nothingness, while elevating form to a position of quasi-autonomy. Avicenna's younger contemporary Avicebron (d. 1058) veered in the other direction, elevating matter at the expense of form. Avicebron's influence may help to explain the willingness of Western scholars (especially Franciscans, such as Richard of Middleton and Duns Scotus) to argue that God can create matter without form.